# Algebraic Geometry Seminar

#### Classification and Birational Rigidity of Del Pezzo Fibrations with an Action of the Klein Simple Group

**Speaker:**
Igor Krylov, University of Edinburgh

**Location:**
Warren Weaver Hall 201

**Date:**
Thursday, March 10, 2016, 3:30 p.m.

**Synopsis:**

Let G be a finite subgroup of the Cremona group. The study of embeddings of G into the Cremona group is equivalent to the study of the G-birational geometry of rational G-Mori fiber spaces. This approach works particularly well for simple subgroups. I prove that any del Pezzo fibration over the projective line with an action of the Klein simple group is either P^{2} x P^{1} or a certain del Pezzo fibration X_{n} of degree 2. The variety X_{n} has 2n quotient singularities of the type 1/2(1,1,1). I prove that the varieties X_{n} are rigid, in particular not rational, for n>2.